Harnack's Inequality for Degenerate and Singular Parabolic Equations by Emmanuel

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Item specifics

Condition
Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See all condition definitionsopens in a new window or tab
ISBN-13
9781489999764
Book Title
Harnack's Inequality for Degenerate and Singular Parabolic Equati
ISBN
9781489999764
Category

About this product

Product Identifiers

Publisher
Springer New York
ISBN-10
1489999760
ISBN-13
9781489999764
eBay Product ID (ePID)
177319482

Product Key Features

Number of Pages
Xiv, 278 Pages
Publication Name
Harnack's Inequality for Degenerate and Singular Parabolic Equations
Language
English
Publication Year
2014
Subject
Differential Equations / General, Differential Equations / Partial, Geometry / Algebraic, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics
Author
Ugo Gianazza, Emmanuele Dibenedetto, Vincenzo Vespri
Series
Springer Monographs in Mathematics Ser.
Format
Trade Paperback

Dimensions

Item Weight
16 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
Dewey Edition
23
Reviews
From the reviews: "Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years, but the issue of the Harnack inequality has remained basically open. In the Introduction to this monograph, the authors present the history of the subject beginning with Harnack's inequality for nonnegative harmonic functions ... . The book is self-contained and addressed to all professionals active in the field, and also to advanced graduate students interested in understanding the main issues of this fascinating research field." (Boris V. Loginov, Zentralblatt MATH, Vol. 1237, 2012)
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515.3534
Table Of Content
Preface.- 1. Introduction.- 2. Preliminaries.- 3. Degenerate and Singular Parabolic Equations.- 4. Expansion of Positivity.- 5. The Harnack Inequality for Degenerate Equations.- 6. The Harnack Inequality for Singular Equations.- 7. Homogeneous Monotone Singular Equations.- Appendix A.- Appendix B.- Appendix C.- References.- Index.
Synopsis
Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p -Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive overview, that would highlight the main issues and also the problems that still remain open. The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p -laplace and porous medium type equations, both in the degenerate ( p >2 or m >1) and in the singular range (1p m The book is self-contained. Building on a similar monograph by the first author, the authors of the present book focus entirely on the Harnack estimates and on their applications: indeed a number of known regularity results are given a new proof, based on the Harnack inequality. It is addressed to all professionals active in the field, and also to advanced graduate students, interested in understanding the main issues of this fascinating research field., Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p -Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive overview, that would highlight the main issues and also the problems that still remain open. The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p -laplace and porous medium type equations, both in the degenerate ( p >2 or m >1) and in the singular range (1< p <2 or 0< m <1), starting from the notion of solution and building all the necessary technical tools. The book is self-contained. Building on a similar monograph by the first author, the authors of the present book focus entirely on the Harnack estimates and on their applications: indeed a number of known regularity results are given a new proof, based on the Harnack inequality. It is addressed to all professionals active in the field, and also to advanced graduate students, interested in understanding the main issues of this fascinating research field.
LC Classification Number
QA370-380

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